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Flavor mixing in quantum field theory and quantum information

Marco Di Mauro

Published May 10, 2011• 0 citations
OpenAlex

Abstract

After reviewing the formalism for describing flavor mixing, both in Quantum Mechanics and Quantum Field Theory, some consequences along three different directions are studied. First, it is proposed that flavor mixing can be a viable candidate for spontaneous supersymmetry breaking, due to the nontrivial vacuum structure induced by it. After the statement of the conjecture, an explicit proof in a simple case is given. Second, the properties of flavor states as entangled states both in QM and QFT are studied. By interpreting such states as multipartite mode–entangled states, both the correlation content and the decoherence effects are studied. Third, a possible new interpretation of flavor mixing as induced by an external vector field is proposed, and it is shown how this solves some problems of the usual formalism in connection with Lorentz and Poincare violation. Some phenomenological consequences of this picture are pointed out, as well as some intriguing physical interpretations.

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After reviewing the formalism for describing flavor mixing, both in Quantum Mechanics and Quantum Field Theory, some consequences along three different directions are studied. First, it is proposed that flavor mixing can be a viable candidate for spontaneous supersymmetry breaking, due to the nontrivial vacuum structure induced by it. After the statement of the conjecture, an explicit proof in a simple case is given. Second, the properties of flavor states as entangled states both in QM and QFT are studied. By interpreting such states as multipartite mode–entangled states, both the correlation content and the decoherence effects are studied. Third, a possible new interpretation of flavor mixing as induced by an external vector field is proposed, and it is shown how this solves some problems of the usual formalism in connection with Lorentz and Poincare violation. Some phenomenological consequences of this picture are pointed out, as well as some intriguing physical interpretations.
The phenomena of particle mixing and flavor oscillations in elementary particle physics are associated with multi-mode entanglement of single-particle states. We show that, in the framework of quantum field theory, these phenomena exhibit a fine structure of quantum correlations, as multi-mode multi-particle entanglement appears. Indeed, the presence of anti-particles adds further degrees of freedom, thus providing nontrivial contributions both to flavor entanglement and, more generally, to multi-partite entanglement. By using the global entanglement measure, based on the linear entropies associated with all the possible bipartitions, we analyze the entanglement in the multiparticle states of two-flavor neutrinos and anti-neutrinos. A direct comparison with the instance of the quantum mechanical Pontecorvo single-particle states is also performed.
The phenomena of particle mixing and flavor oscillations in elementary-particle physics can be addressed from the point of view of quantum information theory, and described in terms of multi-mode entanglement of single-particle states. In this paper we show that such a description can be extended to the domain of quantum field theory, where we uncover a fine structure of quantum correlations associated with multi-mode, multi-particle entanglement. By means of an entanglement measure based on the linear entropies associated with all the possible bipartitions, we analyze the entanglement in the states of flavor neutrinos and antineutrinos. Remarkably, we show that the entanglement is connected with experimentally measurable quantities, i.e. the variances of the lepton numbers and charges.
In the physics of flavor mixing, the flavor states are given by superpositions of mass eigenstates. By using the occupation number to define a multiqubit space, the flavor states can be interpreted as multipartite mode-entangled states. By exploiting a suitable global measure of entanglement, based on the entropies related to all possible bipartitions of the system, we analyze the correlation properties of such states in the instances of three- and four-flavor mixing. Depending on the mixing parameters, and, in particular, on the values taken by the free phases, responsible for the CPCPCP-violation, entanglement concentrates in certain bipartitions. We quantify in detail the amount and the distribution of entanglement in the physically relevant cases of flavor mixing in quark and neutrino systems. By using the wave packet description for localized particles, we use the global measure of entanglement, suitably adapted for the instance of multipartite mixed states, to analyze the decoherence, induced by the free evolution dynamics, on the quantum correlations of stationary neutrino beams. We define a decoherence length as the distance associated with the vanishing of the coherent interference effects among massive neutrino states. We investigate the role of the CPCPCP-violating phase in the decoherence process.
The phenomena of particle mixing and flavor oscillations in elementary-particle physics can be addressed from the point of view of quantum information theory, and described in terms of multi-mode entanglement of single-particle states. In this paper we show that such a description can be extended to the domain of quantum field theory, where we uncover a fine structure of quantum correlations associated with multi-mode, multi-particle entanglement. By means of an entanglement measure based on the linear entropies associated with all the possible bipartitions, we analyze the entanglement in the states of flavor neutrinos and antineutrinos. Remarkably, we show that the entanglement is connected with experimentally measurable quantities, i.e. the variances of the lepton numbers and charges.
Mixing transformations in quantum field theory are nontrivial, since they are intimately related to the unitary inequivalence between Fock spaces for fields with definite mass and fields with definite flavor. Considering the superposition of two neutral scalar (spin-0) bosonic fields, we investigate some features of the emerging condensate structure of the flavor vacuum. In particular, we quantify the flavor vacuum entanglement in terms of the von Neumann entanglement entropy of the reduced state. Furthermore, in a suitable limit, we show that the flavor vacuum has a structure akin to the thermal vacuum of thermo field dynamics, with a temperature dependent on both the mixing angle and the particle mass difference.
Tools of quantum information theory can be exploited to provide a convenient description of the phenomena of particle mixing and flavor oscillations in terms of entanglement, a fundamental quantum resource. We extend such a picture to the domain of quantum field theory where, due to the nontrivial nature of flavor neutrino states, the presence of antiparticles provides additional contributions to flavor entanglement. We use a suitable entanglement measure, the concurrence, that allows extracting the two-mode (flavor) entanglement from the full multimode, multiparticle flavor neutrino states.